Fuchsian polyhedra in Lorentzian space-forms

DOI10.1007/s00208-010-0563-xzbMath1229.52017arXivmath/0702532OpenAlexW2592280817MaRDI QIDQ540429

François Fillastre

Publication date: 3 June 2011

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702532

zbMATH Keywords

Minkowski spacede Sitter spaceanti-de Sitter spaceconvex polyhedral surfaceLorentzian space forms

Mathematics Subject Classification ID

Rigidity results (53C24) Convex sets in (3) dimensions (including convex surfaces) (52A15) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Polyhedral manifolds (52B70)

Related Items (12)

Embeddings of non-positively curved compact surfaces in flat Lorentzian manifolds ⋮ Fuchsian convex bodies: basics of Brunn-Minkowski theory ⋮ Hyperideal polyhedra in the 3-dimensional anti-de Sitter space ⋮ Polyhedra inscribed in a quadric ⋮ Boundary metric of Epstein-Penner convex hull and discrete conformality ⋮ Flippable tilings of constant curvature surfaces ⋮ Polyhedral hyperbolic metrics on surfaces ⋮ Hyperbolic cusps with convex polyhedral boundary ⋮ A Glimpse into Thurston’s Work ⋮ Anti-de Sitter Geometry and Teichmüller Theory ⋮ Gauss images of hyperbolic cusps with convex polyhedral boundary ⋮ Weakly inscribed polyhedra

Cites Work

• Convex polyhedra in Lorentzian space-forms
• Hyperbolic manifolds with convex boundary
• Polyhedral hyperbolic metrics on surfaces
• Hyperbolic cusps with convex polyhedral boundary
• Projective background of the infinitesimal rigidity of frameworks
• Les surfaces euclidiennes à singularités coniques. (Euclidean surfaces with cone singularities)
• Surfaces and planar discontinuous groups. Revised and expanded transl. from the German by J. Stillwell
• A characterization of compact convex polyhedra in hyperbolic 3-space
• Metrics on hyperbolic convex polyhedra
• Réalisations de surfaces hyperboliques complètes dans \(H^3\). (Realizations of complete hyperbolic surfaces in \(H^3\))
• Metrics of constant curvature 1 with three conical singularities on the 2-sphere
• A rigidity criterion for non-convex polyhedra
• The polar dual of a convex polyhedral set in hyperbolic space
• Convex surfaces in Lorentzian spaces of constant curvature
• Convex Fuchs surfaces in Lorentz spaces of constant curvature
• On geometry of convex ideal polyhedra in hyperbolic 3-space
• Polyhedral realisation of hyperbolic metrics with conical singularities on compact surfaces
• Andreev's theorem on hyperbolic polyhedra
• Lorentz spacetimes of constant curvature
• Prescribing Curvature on Compact Surfaces with Conical Singularities
• Small deformations of polygons and polyhedra
• Point Singularities and Conformal Metrics on Riemann Surfaces
• Liouville Equation and Spherical Convex Polytopes
• Sur la rigidité de polyèdres hyperboliques en dimension $3$ : cas de volume fini, cas hyperidéal, cas fuchsien
• Metrics of positive curvature with conic singularities on the sphere
• A Geometrical Background for De Sitter's World
• Geometry and spectra of compact Riemann surfaces
• Voronoi diagrams on piecewise flat surfaces and an application to biological growth
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